Adding another battery under the hood question

I would just tap into the trailer charging line add a fuse and call it good.
If Chevy charge line is not isolated I would add a relay so you can deplete the added battery independent of the start battery.

No, you will not melt any wire from too many cranking amps available.

The existing wire size and length will typically limit the voltage/amps that go into the house batteries. Worst case you need to replace a fuse.